Sets of Fractional Dimensions (IV): On Rational Approximation to Real Numbers
Sets of Fractional Dimensions (IV): On Rational Approximation to Real Numbers
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DOI：
10.1112/jlms/s1-9.2.126
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发表时间：
1934-04
影响因子：
1.2
通讯作者：
A. Besicovitch
中科院分区：
文献类型：
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作者：
A. Besicovitch
1.对任何真实的数r，存在无穷多个有理逼近min，其误差小于n-2，这是一个众所周知的结果。本文的问题是研究具有较强有理逼近的真实的数的集合。这个问题的解自然会用分数维的集合来给出。设Eq，q> 2，是区间（0，1）的真实的数r的集合，对于该集合，不等式由无穷多个有理数min满足。我们将证明
1. It is a well-known result that there exist infinitely many rational approximations min to any real number r with an error less than n-2• The problem of this article is the study of the sets of real numbers with stronger rational approximations. The solution of this problem will naturally be given in terms of sets of fractional dimensions*. Let Eq, q> 2, be the set of real numbers r of the interval (0, 1) for which the inequality is satisfied by infinitely many rational numbers min. We shall prove the